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Assessment of variance components in nonlinear mixed-effects elliptical models


  • Cibele Russo


  • Reiko Aoki


  • Gilberto Paula



The issue of assessing variance components is essential in deciding on the inclusion of random effects in the context of mixed models. In this work we discuss this problem by supposing nonlinear elliptical models for correlated data by using the score-type test proposed in Silvapulle and Silvapulle ( 1995 ). Being asymptotically equivalent to the likelihood ratio test and only requiring the estimation under the null hypothesis, this test provides a fairly easy computable alternative for assessing one-sided hypotheses in the context of the marginal model. Taking into account the possible non-normal distribution, we assume that the joint distribution of the response variable and the random effects lies in the elliptical class, which includes light-tailed and heavy-tailed distributions such as Student-t, power exponential, logistic, generalized Student-t, generalized logistic, contaminated normal, and the normal itself, among others. We compare the sensitivity of the score-type test under normal, Student-t and power exponential models for the kinetics data set discussed in Vonesh and Carter ( 1992 ) and fitted using the model presented in Russo et al. ( 2009 ). Also, a simulation study is performed to analyze the consequences of the kurtosis misspecification. Copyright Sociedad de Estadística e Investigación Operativa 2012

Suggested Citation

  • Cibele Russo & Reiko Aoki & Gilberto Paula, 2012. "Assessment of variance components in nonlinear mixed-effects elliptical models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 519-545, September.
  • Handle: RePEc:spr:testjl:v:21:y:2012:i:3:p:519-545 DOI: 10.1007/s11749-011-0262-2

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    References listed on IDEAS

    1. Patriota, Alexandre G., 2011. "A note on influence diagnostics in nonlinear mixed-effects elliptical models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 218-225, January.
    2. Jan R. Magnus & Andrey L. Vasnev, 2007. "Local sensitivity and diagnostic tests," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 166-192, March.
    3. Zaixing Li & Lixing Zhu, 2010. "On Variance Components in Semiparametric Mixed Models for Longitudinal Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 442-457.
    4. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
    5. Cysneiros, Francisco Jose A. & Paula, Gilberto A., 2005. "Restricted methods in symmetrical linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 689-708, June.
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    Cited by:

    1. Zaixing Li & Fei Chen & Lixing Zhu, 2014. "Variance Components Testing in ANOVA-Type Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 482-496, June.
    2. Li, Zaixing, 2015. "A residual-based test for variance components in linear mixed models," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 73-78.
    3. Chen, Fei & Li, Zaixing & Shi, Lei & Zhu, Lixing, 2015. "Inference for mixed models of ANOVA type with high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 382-401.
    4. repec:spr:testjl:v:26:y:2017:i:4:d:10.1007_s11749-017-0532-8 is not listed on IDEAS
    5. repec:spr:sankhb:v:79:y:2017:i:1:d:10.1007_s13571-016-0116-8 is not listed on IDEAS


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